The world population at the beginning of 1990 was 5.3 billion. Assume that the p

Question

The world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at the rate of approximately 2%/year and find the function Q(t) that expresses the world population (in billions) as a function of time t (in years), with t = 0 corresponding to the beginning of 1990. (Round your answers to two decimal places.) (a) If the world population continues to grow at approximately 2%/year, find the length of time t0 required for the population to quadruple in size. t0 = yr (b) Using the time t0 found in part (a), what would be the world population if the growth rate were reduced to 1.1%/yr?

Explanation / Answer

The population is compunding at 2 % per yeat

Hence Q(t) = Q(0)*(1+ (r/100)t
Q(t) = 5.3*(1.02)t

Now we have Q(t0) = 5.3*4
Hence 5.3*4 = 5.3*(1.02)t
Hence : t0 = 70.0056 years 70 years

Hence with 1.1% growth rate Q(70) = 5.3*(1.011)70 = 11.399 billion

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